Video Lectures

Lower bounds on the size of semidefinite programming relaxations

November 30, 2015

We introduce a method for proving lower bounds on the efficacy of semidefinite programming (SDP) relaxations for combinatorial problems. In particular, we show that the cut, TSP, and stable set polytopes on $n$-vertex graphs are not the linear image...

video lecture

Hausdorff dimension of Kleinian group uniformization of Riemann surface and conformal rigidity

November 24, 2015

Yong Hou

For this talk I'll discuss uniformization of Riemann surfaces via Kleinian groups. In particular question of conformability by Hasudorff dimension spectrum. I'll discuss and pose some questions which also in particular will imply a conjecture due to...

video lecture

General systems of linear forms: equidistribution and true complexity

November 24, 2015

Pooya Hatami

Higher-order Fourier analysis is a powerful tool that can be used to analyse the densities of linear systems (such as arithmetic progressions) in subsets of Abelian groups. We are interested in the group $\mathbb{F}_p^n$, for fixed $p$ and large $n$...

video lecture

Fun with finite covers of 3-manifolds: connections between topology, geometry, and arithmetic

November 23, 2015

Nathan Dunfield

Following the revolutionary work of Thurston and Perelman, the topology of 3-manifolds is deeply intertwined with their geometry. In particular, hyperbolic geometry, the non-Euclidean geometry of constant negative curvature, plays a central role. In...

video lecture

Advances on Ramsey numbers

November 23, 2015

Jacob Fox

Ramsey theory refers to a large body of deep results in mathematics whose underlying philosophy is captured succinctly by the statement that "Every very large system contains a large well-organized subsystem." Ramsey numbers capture how very large...

video lecture

Geometric deformations of orthogonal and symplectic Galois representations

November 19, 2015

Jeremy Booher

For a representation of the absolute Galois group of the rationals over a finite field of characteristic $p$, we would like to know if there exists a lift to characteristic zero with nice properties. In particular, we would like it to be geometric...

video lecture

Cohomology for computer science II

November 17, 2015

Alex Lubotzky

We will start with presenting the basic notions of (co)homomology of simplical complexes (which requires only basic linear algebra over the field of order 2) and then we will indicate its relevance for several topics in computer science and...

video lecture

The complex geometry of Teichmüller spaces and bounded symmetric domains I & II

November 17, 2015

Stergios Antonakoudis

video lecture

Welcome and Introduction

November 17, 2015

https://www.ias.edu/gr100 Albert Einstein’s general theory of relativity, a pillar of modern physics formulated 100 years ago, will be celebrated by the Institute for Advanced Study and Princeton University in a two-day conference, General...

video lecture

Cohomology for computer science

November 17, 2015

Alex Lubotzky